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INGE LEHMANN

13 May 1888-21 February 1993

Elected For.Mem.R.S. 1969

BY BRUCE A. BOLT

University of California, Berkeley, Seismographic Station,

475 Earth Sciences Building, Berkeley, CA 94720, USA

FAMILY AND EDUCATION

Dr Inge Lehmann was born on 13 May 1888 at Osterbro by the Lakes in Copenhagen. She grew up and lived much of her long life there, and for over 50 years, on Kastelvej, Copenhagen. The Lehmann family had its roots in Bohemia; the Danish branch had many influential members of high standing, including barristers, politicians and engineers. Inge Lehmann's paternal grandfather laid out the first Danish telegraph line (opened in 1854) and her great grandfather was Governor of the National Bank. Her mother's father, Hans Jakob Tørsleff, belonged to an old Danish family with a priest in every generation. A granddaughter, Anne Groes, was for a while Minister of Commerce. Inge's childhood was a happy one in the peaceful atmosphere of the 1890s. Her father, Alfred Lehmann, was a professor of psychology at the University of Copenhagen who pioneered the study of experimental psychology in Denmark. He was rarely seen except at mealtimes, though sometimes on Sunday he took the family for a walk. (A fund endowed by her estate makes a travel award each year alternatively to a psychologist and a geophysicist.) She had a sister, Harriet.

Inge was sent by her parents to an enlightened co-educational school run by Hannah Adler, an aunt of Niels Bohr. She learnt there that boys and girls could be treated alike for work and play: 'No difference between the intellect of boys and girls was recognized, a fact that brought some disappointments later in life when I had to recognize that this was not the general attitude' (quoted in Brush 1980). The teacher of mathematics stood out, sometimes encouraging Inge's interest by giving her special problems to solve. Her parents, however, objected to this, because at that time she did not seem strong enough for extra work. Lehmann later remarked (autobiographical notes), 'They could not be expected to understand, I suppose, that I should have been stronger if I had not been so bored with school work.' She left this splendid Faellesskole in July 1906 after having passed the university entrance examination with the distinction of first class.

She entered the University of Copenhagen in the autumn of 1907 and studied mathematics, aiming at cand. mag. (candidata magisterii), for which she also needed physics, chemistry and astronomy. She passed the first part of the examination in 1910 and, in the autumn, was admitted to Newnham College, Cambridge, for a one-year stay. Harold Jeffreys (1891-1989) was at St John's College, Cambridge, at the same time, but the two evidently did not know each other at that time (Lady Jeffreys, personal communication). She enjoyed her stay 'in spite of the severe restrictions inflicted on the conduct of young girls, restrictions completely foreign to a girl who had moved freely amongst boys and young men at home'. Her stay was prolonged because of the possibility of entering for the Mathematical Tripos. However, serious overwork from accelerated study to pass the entrance examinations led to her return home in December 1911. Her recovery was slow, and for a long time she could not consider resuming her university studies.

For some years she worked in an actuary's office where she acquired considerable training in computations. In the autumn of 1918 she re-entered the University of Copenhagen and graduated in the summer of 1920. In February 1923, she became assistant to the professor in actuarial science at the University for three years and during that time acquainted herself with the theory of observations.

In 1925, she was appointed assistant to Professor N.E. Norlund, who in the capacity of Director of 'Gradmaalingen', was planning to have seismographic stations installed near Copenhagen and in Ivigtut and Scoresbysund in Greenland. In this fortuitous way she entered the discipline of seismology, a rare profession in aseismic Denmark.

I began to do seismic work and had some extremely interesting years in which I and three young men who had never seen a seismograph before were active installing Wiechert, Galitzin-Wilip and Milne-Shaw seismographs in Copenhagen and also helping to prepare the Greenland installations. I studied seismology at the same time unaided, but in the summer of 1927 I was sent abroad for three months. I spent one month with Professor Beno Gutenberg in Darmstadt. He gave me a great deal of his time and invaluable help. I paid short visits to Professor E. Tams in Hamburg, to Professor E. Rothe in Strasbourg, Dr van Dijk in De Bilt and Dr Somville in Uccle. Everywhere I was very kindly received and given much information.

These men were, at the time, the leading practitioners of seismology in Europe. Gutenberg was especially notable, already in 1914 having used recordings of distant earthquakes to infer an average depth of 2900 km to the boundary of the Earth's central core (Gutenberg 1914). (The present estimate is 2885 3 km.)

CAREER IN DENMARK

In the summer of 1928, Lehmann passed an examination in geodesy at the University of Copenhagen, her thesis having a seismological subject, and obtained the degree mag. scient. (magister scientiarum). In 1928 she was appointed chief of the seismological department of the newly established Royal Danish Geodetic Institute, a post she held until her retirement in 1953. Her responsibilities included maintaining what turned out to be the very reliable and internationally important seismographic observatories of Copenhagen, Ivigtut and Scoresbysund. Each of them had a caretaker whom she had to instruct. The caretakers of the Scoresbysund station were a special concern. They did not stay for many years running, and the connection with the station in those days was by a boat calling in once a year.

At the Copenhagen observatory Lehmann had to keep the instruments properly adjusted (3-*Numbers in this form refer to the bibliography at the end of the text.) and to see to the maintenance and repairs of the establishment, including the buildings. The key to her unequalled knowledge of the seismic wave patterns recorded from very distant earthquakes by the seismographs of the Danish network was established early, because it fell on her to interpret the seismograms and to publish the station bulletins of the measurements. She was free to do scientific work, but it was not considered a duty and it was not encouraged. Sometimes she had assistants, but more often not, not even for office work.

When Inge Lehmann began her research, she realized that the determination of earthquake epicentre parameters was not reliable. To minimize the reading errors in reported arrival times of seismic waves, she correlated by eye similar wave forms between different seismograms (1, 2, 5). In this way, phases could be matched clearly and robust interpretations obtained. Characteristically modest, Lehmann wrote in her biographical notes, 'The most important result arrived at was that the presence of a distinct inner core was required for the interpretation of some phases recorded at great epicentral distances.' This jewel in her observational crown is discussed below, but Lehmann's important work was not confined to her discovery of the inner core. Her publications list from her Danish Institute years contains 35 papers, many in Danish publications and reports of the Geodetic Institute. Her first paper appeared in 1926, on the accuracy of interpolation.

In the last half of the 19th century, routine readings of seismograms were made for each substantial earthquake at observatories around the world and collected by mail for publication in the International Seismological Summary (ISS) at Kew, England. It was crucial to know the relative accuracy of measurements from each station before geological inferences could be based on them. In reaction to this need Lehmann made an early determination (4, 11) of the reliability of European seismological stations; she became interested in the various manners in which records were interpreted and discussed how the most useful readings could be obtained. Northern Europe is not earthquake country, so like many of her seismological contemporaries in Europe, she turned to the study of small local earthquakes and explosions (5, 10), and the striking microseismic wave motions (12, 13) generated by Arctic and North Sea storms.

In her last publication (28), Lehmann gives valuable reminiscences of her professional work at the Copenhagen Observatory. She points out the difficulty of seismologists at that time determining the epicentres of teleseisms. She comments, 'As a result of many considerations it was found that while a group of stations did not allow travel times to be accurately determined, it made it possible to determine the slope of the travel time. In modern technology, it might be said the European stations were used as an array.' She entered into a 'lively' correspondence with Harold Jeffreys during the period in which he and K.E. Bullen were calculating their famous seismological travel-time curves (Jeffreys & Bullen 1935). Like Jeffreys, she also had an early and substantial lifetime interest in the seminal problem of determining the travel-time curves of various types of seismic waves through the Earth (6, 7, 9). In sharp contrast with the theoretical power of these two mathematicians, who reduced the published ISS sets of arrival-time readings of others, Lehmann, like Gutenberg, brought to bear the sharp observational insight provided by the seismographic patterns themselves.

Students entering seismology now may find it hard to appreciate the early difficulty in bootstrapping from the crudest values to the highly precise and robust modern travel-time tables. Nowadays the concern in this research field has shifted to making second order, regional and frequency-dependent adjustments to established curves.

The dark years of the Second World War stifled the traditional international exchange of earthquake observations from the largely serendipitous global network of seismographic stations. Yet at many observatories, such as Copenhagen, routine maintenance and reading of earthquake waves continued.

As the postwar burden lifted, a fertile new turn in Lehmann's research occurred when Professor Maurice Ewing, Director of the Lamont Geological Observatory (L.G.O.) of Columbia University, came to visit the Copenhagen seismological station in 1951. He was enormously impressed by her expertise and he invited her to come to L.G.O. to study a newly defined seismic phase called 'Lg' that he and Professor Frank Press had found in American records. Her consequent visit to L.G.O. for several months in 1952 (see below) was to be followed after her retirement by many more to Lamont and other earthquake observatories in the USA and Canada.

She investigated observationally existence criteria for the Lg surface wave phase (14, 17) and became greatly impressed by the various surface wave studies and wave-guide approach of Ewing and Press. She did not, however, have the background for the theoretical side of wave-guide propagation and so continued her reliance on careful measurements of body-wave amplitudes and travel times. This part of observatory seismology is less tractable than surface wave analysis. Moreover, like all seismologists up till about 1960, she was severely handicapped by the heterogeneity and lack of coordination of seismographs in the first five decades of the century.

PROFESSIONAL ACTIVITIES

By its nature, the science of seismology demands intra- and international cooperation. Lehmann soon became one of the central pillars of international seismological activities. In 1931 she attended the Centenary Meeting of the British Association in London and, in 1938, the Association meeting in Cambridge. In September 1936 she participated in the Assembly of the International Union of Geodesy and Geophysics (I.U.G.G.) in Edinburgh and afterwards returned to Cambridge for about 3 months' work. In 1947 the deliberate large-size chemical explosion at Heligoland was recorded by the Danish seismographs, and she was invited to present her measurements at a November meeting of the Royal Society and at a subsequent meeting on the same experiment in Cambridge. She stayed on in Cambridge working for about 2 months.

She became a regular Danish delegate and contributor at the I.U.G.G. Assemblies (Prague 1927, Stockholm 1930, Edinburgh 1936, Oslo 1948, Brussels 1951, Rome 1954, Toronto 1957, Berkeley 1963 and Zurich 1967). The Instituto Nazionale de Geofisica invited her to an important seismological meeting in Verona in 1950, at which the delegates formed the European Seismological Federation. Its form was not approved, however, by the I.U.G.G., and in 1951 it was replaced by the still-flourishing European Seismological Commission (E.S.C.) under the auspices of the International Association of Seismology and Physics of the Earth's Interior (I.A.S.P.E.I.). She presented papers at many subsequent meetings of the E.S.C.

In 1952 she spent several months at the L.G.O. and went on to short visits to the observatories at Tucson, Pasadena, Berkeley, Saint Louis and Washington. She was at the Dominion Observatory, Ottawa, working for 3 weeks in August 1954 and for 2 months in the summer of 1957. She was at the L.G.O. working for about 6 months in 1957-58 and for a month and a half in the spring of 1960. In 1962-64 she returned there in three periods, in all for about 17 months. By this time, Lehmann's scientific reputation began to be appropriately recognized, and in 1964 she was awarded the prestigious Emil Wiechert Medal of the Deutsche Geophysikalische Gesellschaft. She went back to North America in 1964-65, spending 4 and a half months at Ottawa, and to L.G.O. again in December 1968, where she stayed for 5 months. After three visits to the Seismographic Stations of the University of California at Berkeley in 1952, 1954 and 1965, she undertook more sustained research there for 3 and a half months in the winter and spring of 1968, when she became a favourite of graduate students. She had written in 1965, saying that when she was at Berkeley for the I.U.G.G. in 1963, she had been assigned noisy accommodation. For this reason, a room was secured at the Women's Faculty Club, a quiet lovely site at the centre of campus. She made many friends at this institution.

In the early 1960s a critical discussion emerged on upgrading the ISS, at that time many years in arrears and underfunded. She was active in the establishment of its successor, the International Seismological Centre (I.S.C.) in Edinburgh. She took part in the 1961 Paris Meeting of the ISS Committee and attended ISS Advisory Committee meetings until the 1967 I.U.G.G. Assembly at which she resigned.

RETIREMENT YEARS: HER NEW RESEARCH PHASE

Lehmann retired from her post at the Geodetic Institute in 1953, 5 years before the mandatory retirement age of 70. She states in her autobiographical notes that afterwards she planned to use the freedom from routine for a continuation of her seismological studies. In his personal obituary, delivered at the Lehmann home on Kastelvej, her cousin's son Nils Groes comments:

This was probably the first time that she felt really free ... she was first recognized abroad where she received several academic distinctions. But equally, Inge was pleased by the international academic friendships which she nursed up to her death. The Danish recognition did not arrive until late. However, it was appreciated.

The award of its Bowie Medal to Lehmann by the American Geophysical Union in 1971 was a milestone in the establishment of her distinction. Professor Francis Birch gave an acute and gracious citation:

The Lehmann discontinuity was discovered through exacting scrutiny of seismic records by a master of a black art for which no amount of computerization is likely to be a complete substitute... Since her retirement from the Geodetic Institute, Dr Lehmann has increased her rate of publication, which is understandable since she no longer has to worry about keeping someone on the job at Scoresbysund!

It happened that her 'retirement' from formal observatory responsibilities at Copenhagen coincided with a dramatic upswing in the quantity and quality of seismological activities worldwide. At the time Lehmann began planning her retirement studies, global stations had declined in number and often quality. The Depression and the Second World War had seen only the barest financial support, and seismographic recording became an unimportant sideline at astronomical observatories. There was a hodgepodge of seismographs recording on smoked or photographic paper, responding to waves in different frequency ranges and recording at various rates. Few instruments were calibrated so that the actual motion of the ground could not be measured, let alone frequency-domain analyses of the wave spectra.

Every empirical science requires for its progress adequate observational equipment, and by the 1950s, seismologists looked with envy at the postwar growth of high-energy physics laboratories and of sophisticated radio-astronomy observatories. Rather suddenly and unexpectedly, a major stimulus for seismology came, not from demands for reduction of earthquake risk, but from the problem of surveillance of clandestine underground nuclear explosions (Bolt 1976). A high-level conference of experts from the nuclear powers at Geneva in 1958 produced a discouraging evaluation of seismological reading capability. President Eisenhower was prompted to set up a Panel of Seismic Improvement, called after its Chairman, Lloyd Berkner. It was charged with reviewing the feasibility of improving seismic surveillance of secret explosions and of promoting research in seismology, particularly in the United States, related to the detection and identification of underground nuclear explosions. One critical consequence in the United States was a jump in expenditure in a research programme called VELA UNIFORM. This programme and parallel efforts in other countries aimed at the development of improved, standardized seismographs. These new recorders were installed in the early 1960s at about 200 existing seismographic stations around the world as the Worldwide Standardized Seismographic Network (WWSSN). (Copenhagen was one of these.)

Instrumentation for the WWSSN consisted of six calibrated, optically recording seismographs: one set of three short-period seismographs and one set of three long-period seismographs. The frequency-response curves for all of these instruments were carefully measured. The all-important time accuracy was obtained by means of standard crystal clocks, precise to one part in lO6.

By 1960, records from the WWSSN were becoming available to the seismological community with no publication restrictions and were easily obtained from the US Coast and Geodetic Survey data centre in Washington, D.C. The new seismograms permitted a keen observer like Lehmann to undertake much more precise measurements and analysis of earthquake phases than had been possible before. It is important therefore to remember that after 1960 her research on correlating readings and wave forms was based on this upgraded WWSSN network. Lehmann's unparalleled experience in reading seismograms was looked to immediately in the United States as a great resource in attempts to achieve the goals of the VELA UNIFORM programme.

Perhaps Lehmann's first important research abroad was a continuation of her studies of seismic body waves during 4 months in 1954 working with one of her early seismological mentors, Professor Beno Gutenberg (by this time Director of the Seismological Laboratory at the California Institute of Technology at Pasadena). She made a careful study of travel times for small epicentral distances. However, travel times differ regionally, and she demonstrated that a low-velocity layer for P in the upper mantle, postulated by Gutenberg elsewhere, was not in evidence for Europe and northeastern America (16). She endeavoured to find a velocity structure that would fit revised travel times of Jeffreys by assuming the existence of a strong, possibly abrupt, velocity increase at a depth somewhat greater than 200 km (18). This model was designed initially to replace the 400 km depth discontinuity derived from the Jeffreys-Bullen tables. Her '220 km discontinuity' came to play an important role in subsequent modelling of the upper mantle by others (Anderson 1981). From assumed velocity structures that included it, Lehmann calculated travel times in close agreement with various sets of seismograph readings. The travel times of some well-recorded European earthquakes were first considered, but later she made extensive use of explosion records (20, 22) to demonstrate clear evidence of it in some regions. However, even at the end of her career, the uneven geographical nature of seismological measurements precluded any conclusion on the full angular extent of the 220 km and 400 km discontinuities (27).

She extended her studies (19) to those of S waves as recorded in Europe. Because S waves always arrive as superposed and converted signals on the P wave trains, their discrimination is much more difficult. Nevertheless, she succeeded in explaining the presence of two S phases in European records at small epicentral distances. A comprehensive account of all these body-wave studies on low-velocity layers and discontinuities in the upper mantle was published (21). Subsequently, she continued such body-wave studies by examining the new evidence for the 400 km discontinuity (24, 26). She found it to be very clear in some regions, but poorly recorded or absent in others.

One of the research centres she enjoyed most was Lamont Geological Observatory (now Lamont-Doherty Earth Observatory). It was then in its heyday of innovation in seismology under the directorship of Maurice Ewing (1906-1974). Ewing was a close friend and admirer of Inge Lehmann, and he made possible several of her visits to Lamont through Harry Oscar Wood awards of the Carnegie Institution of Washington. In a personal letter to Lady Jeffreys (12 June 1974) from Denmark soon after Ewing's death, Lehmann expressed her debt and affection:

I was profoundly shaken by the death of Maurice Ewing. It is very sad that his activities should be cut off so early. I admired him immensely, but to me he was not only the great scientist, he was also a wonderful friend. He invited me to come to Lamont in the first place, and it was due to his encouragement and support that I could continue to work for many years under better conditions than I had ever known before. The last chapter of my life became interesting and very pleasant. Reviewing now the events of those 20 years, I feel more keenly than ever what I owe to him. In Galveston [Ewing transferred in 1972 to the University of Texas] he was far away but his death evoked in me a curious feeling of loneliness. No one here knows much about him, no one has any idea of what he has done for me-so there is no one to talk to about him. It was very nice indeed to get your letter.

Initially, her interest in the Lg phase drew her to Lamont. She brought earthquake records from Europe and determined travel times and other features of Lg. It was at Lamont in 1960 that I first had an opportunity to discuss seismology with Inge Lehmann, and I was at once struck by the deep seismological knowledge that she had regarding seismograms and their wave patterns.

By now over 70 years of age, Lehmann became greatly stimulated by the seismological challenges and opportunities of the VELA UNIFORM programme. With financial support from this source, she turned to probe the structure of the upper mantle, using the seismic body waves recorded from underground nuclear explosions (23, 25). These studies involved interpretations of seismograms containing complicated reflected seismic phases. She advocated the reading of such records by one person, ' [who] paid attention to the shape of the curves so that it might be possible to trace a phase from one station to another one, and in this way determine a time curve which was not otherwise observable'. Her critical approach to science was exemplified by her pointing out the dangers of reading phases where they are Bullen tables. Her '220 km discontinuity' came to play an important role in subsequent modelling of the upper mantle by others (Anderson 1981). From assumed velocity structures that included it, Lehmann calculated travel times in close agreement with various sets of seismograph readings. The travel times of some well-recorded European earthquakes were first considered, but later she made extensive use of explosion records (20, 22) to demonstrate clear evidence of it in some regions. However, even at the end of her career, the uneven geographical nature of seismological measurements precluded any conclusion on the full angular extent of the 220 km and 400 km discontinuities (27).

She extended her studies (19) to those of S waves as recorded in Europe. Because S waves always arrive as superposed and converted signals on the P wave trains, their discrimination is much more difficult. Nevertheless, she succeeded in explaining the presence of two S phases in European records at small epicentral distances. A comprehensive account of all these body-wave studies on low-velocity layers and discontinuities in the upper mantle was published (21). Subsequently, she continued such body-wave studies by examining the new evidence for the 400 km discontinuity (24, 26). She found it to be very clear in some regions, but poorly recorded or absent in others.

One of the research centres she enjoyed most was Lamont Geological Observatory (now Lamont-Doherty Earth Observatory). It was then in its heyday of innovation in seismology under the directorship of Maurice Ewing (1906-1974). Ewing was a close friend and admirer of Inge Lehmann, and he made possible several of her visits to Lamont through Harry Oscar Wood awards of the Carnegie Institution of Washington. In a personal letter to Lady Jeffreys (12 June 1974) from Denmark soon after Ewing's death, Lehmann expressed her debt and affection:

I was profoundly shaken by the death of Maurice Ewing. It is very sad that his activities should be cut off so early. I admired him immensely, but to me he was not only the great scientist, he was also a wonderful friend. He invited me to come to Lamont in the first place, and it was due to his encouragement and support that I could continue to work for many years under better conditions than I had ever known before. The last chapter of my life became interesting and very pleasant. Reviewing now the events of those 20 years, I feel more keenly than ever what I owe to him. In Galveston [Ewing transferred in 1972 to the University of Texas] he was far away but his death evoked in me a curious feeling of loneliness. No one here knows much about him, no one has any idea of what he has done for me-so there is no one to talk to about him. It was very nice indeed to get your letter.

Initially, her interest in the Lg phase drew her to Lamont. She brought earthquake records from Europe and determined travel times and other features of Lg. It was at Lamont in 1960 that I first had an opportunity to discuss seismology with Inge Lehmann, and I was at once struck by the deep seismological knowledge that she had regarding seismograms and their wave patterns.

By now over 70 years of age, Lehmann became greatly stimulated by the seismological challenges and opportunities of the VELA UNIFORM programme. With financial support from this source, she turned to probe the structure of the upper mantle, using the seismic body waves recorded from underground nuclear explosions (23, 25). These studies involved interpretations of seismograms containing complicated reflected seismic phases. She advocated the reading of such records by one person, ' [who] paid attention to the shape of the curves so that it might be possible to trace a phase from one station to another one, and in this way determine a time curve which was not otherwise observable'. Her critical approach to science was exemplified by her pointing out the dangers of reading phases where they are expected at be: 'If the readings are adapted to time curves already existing, they are not very useful.' Professor Jack Oliver (personal communication), who was closely associated with Lehmann at Lamont, has written:

Her work with nuclear explosions was important, not so much because she found something new but because her stature and her integrity provided respectability and credibility for those whose studies she presented support for. This was not a trivial point in the partly-political, as opposed to purely-scientific, atmosphere during the time when the nuclear test-ban treaty was a hot political topic. Lesser-known seismologists could be suspected of warping results to support a particular political point of view.

DISCOVERY OF THE EARTH'S INNER CORE

The 50th anniversary of the discovery of the Earth's inner core in 1936 by Inge Lehmann was marked by a symposium and special publications (Bolt 1987). Her proposal, published in the Bureau Central Seismoloque International, Travaux Scientifique (8) was intended as a way to avoid difficulties that had arisen in interpreting the observed arrivals of seismic core waves when only a unitary terrestrial core was assumed. Examples of the recorded wave forms available to her in 1936 and the simple Earth model used in her argument are shown in figure 1.

Early seismological observations showed an observational shadow of P wave arrivals


Figure 1. The seismological discovery of the earth's inner core. From I. Lehmann, P', Bureau Central Seismologique International, Series A, Travaux Scientifiques, 14, 88, 1936.

beyond epicentral distances of 105° or so. Yet on the other side of the Earth, particularly at distances near 140°, unidentified seismic wave onsets were seen from earthquakes out to the antipodes. These unidentified waves were of P type, but were delayed by 5 min after the times predicted by the simple extrapolation of the Jeffreys-Bullen (1935) P travel-time curve for 0° to 105°.

A unitary core was first proposed on seismological evidence by R.D. Oldham to explain these features (Brush 1980). Inside its outer boundary the seismological travel times entailed a sharp drop in seismic P wave velocity. Rays in such a central core are called PKP and their paths may be followed in figure 1. The ray that just grazes the core emerges at the surface as a tangent to it (Ray 2) or is refracted back to beyond 180° (Ray 2a). As these PKP rays become steeper they refract back to shorter distances until at an angle of about 142° (Ray 3) they cease their backward regression and there is an optical caustic. Steeper and steeper rays then progress again in a normal way to greater and greater distances (Rays 4 and 6), until at last the diametrical ray passes to the antipodes.

The improved seismographs of the 1920s and 1930s enabled observers such as Lehmann to spot additional waves in a distance gap between 105° and 142° that could not be explained on the unitary-core model. (The arrows in the figure on the east and vertical component seismograms at two northern stations indicate PKP waves identified by Lehmann.) Various ideas were floated to account for the unexpected onsets, notably that such seismic energy was due to diffraction of the seismic waves at the 142° caustic. (Later, Harold Jeffreys (1939) demonstrated that the diffraction hypothesis was theoretically untenable.)

As already mentioned, Inge Lehmann was in an excellent situation to become familiar with these seismic wave phases because her far-flung Danish seismographic network, as well as other European stations, was located at large epicentral distances from energetic earthquake sources in the South Pacific.

For example, a damaging earthquake on 16 June 1929 in New Zealand was well-recorded by European seismographs. Lehmann, in comparing a number of these recordings, could clearly see onsets of PKP waves. Such evidence enabled her to make the necessary imaginative jump (8):'

An explanation of the P3' wave (now denoted PKIKP) is required, since now it can hardly be considered probable that it is due to diffraction. A hypothesis will be here suggested which seems to hold some probability, although it cannot be proved from the data at hand.

The strength of Lehmann's argument was buttressed by her ability to discard unessential information. She assumed a simple two-shell Earth model, as shown in figure 1, with constant seismic P velocities in the mantle (10 km s-t) and in the core (8 km s-1). These were reasonable average values for both shells. She then introduced a small central core, again with a constant P velocity. Such simplifications entailed straight seismic rays (chords) rather than curved paths, thus permitting the calculation of the wave travel times by elementary trigonometry. Lehmann then proceeded by successive adjustments to show that a reasonable velocity (10 km s-1) and radius of the inner core (1400 km) could be found that predicted a travel-time curve close to the actual observations of the travel times of the core waves (P3') in question (i.e. Ray 5 in figure 1).

In effect, Lehmann proved an existence theorem: namely, a plausible tripartite Earth structure could be found that explained the main features of the observed core waves. However, she did not go on to solve the inverse problem; that is, having proved the existence theorem, she did not use her measurements of travel times to estimate statistically the inner core parameters that satisfied them within the measurement uncertainties.

This final step was done first two years later by Gutenberg and Richter (1938) who inferred an inner core radius of about 1200 km and a mean inner core P velocity of 11.2 km s-1. They argued, however, that, 'Both observed amplitudes and travel times, suggest a rapid but continuous increase in velocity in a particular narrow range ... within the core rather than the discontinuity. Moreover, no reflective waves have been found, such as would correspond to a discontinuity.' In a parallel programme of inferring this interior terrestrial structure, Harold Jeffreys (1939), after first giving a crucial test indicating decisively that the diffraction interpretation for the P3' phases was unacceptable, adopted the Lehmann inner-core hypothesis and obtained a satisfactory numerical inversion of his PKP travel-time dataset. But, unlike Gutenberg and Richter, he retained Lehmann's sharp boundary. 'The opinion of Lehmann and Gutenberg and Richter that PKP between 110-142° is refracted at an inner core is therefore substantiated.' It is notable, however, that for over 20 years after this adoption of an inner core model, the rate of increase of velocity at the inner core boundary remained highly controversial.

Subsequently, independent arguments by Birch (1940) and Bullen (1946) established that the rapid increase in P velocity at the inner core boundary entailed a transition from liquid to solid conditions, with a jump in shear wave velocity from zero to about 3.1 km s-1, if the pressure-induced gradient in incompressibility was to be plausible. It was not until 1962 (Bolt 1962) that direct new evidence supporting Lehmann's sharp boundary was advanced, and not until 1970 that high-angle reflections (PKiKP) of seismic P waves incident on the inner core were observed unequivocally on seismograms (Engdahl et al. 1970). Later it was shown (Bolt & Qamar 1970) that the high-frequency reflections PKiKP (and possibly the doubly internally reflected PKIIKP wave) at steep incident angles on the inner-core boundary are evidence for jumps in both density and incompressibility at the boundary. These inferences have been supported closely by recent Earth model inversions using higher modes of terrestrial eigen-vibrations (Dziewonski & Anderson 1981). An account of the studies of the inner core up to the late 1980s can be found in Bolt (1987). In this decade, the properties of the inner core remain a strong attractor of seismological research. Lehmann would no doubt have been delighted to assess the recent evidence for significant anisotropy in the inner core (Tromp 1995) and for its rotation relative to the outer core (Song & Richards 1996).

In 1986, during the special symposium at the American Geophysical Union Annual Meeting in her honour (Bolt 1987), she wrote to me, 'I was, of course, aware that it was 50 years since I discovered the core but I did not pay much attention to the fact. I see now that I will have to take the anniversary more seriously.'

PERSONALITY AND ACHIEVEMENTS

In the history of seismology, the life of Inge Lehmann will be marked in very special ways. Her work was a product of several qualities of a remarkable woman. She was a dedicated and thorough observational seismologist. She had a highly critical and independent mind and the capacity to work out, in quantitative ways, the implications of alternative models. She could cut through the complications to the core of the problem. There can be little doubt that, as a lone woman working in seismology at that time, she needed strong resources of character to sustain her high motivation and curiosity.

Nils Groes has painted a memorable picture:

Inge's grown-up life was characterized by hard work, tough grind, a magnificent scientific effort and, finally, great academic appreciation... I remember Inge one Sunday in her beloved garden on Søbakkevej; it was in the summer, and she sat on the lawn at a big table, filled with cardboard oatmeal boxes. In the boxes were cardboard cards with information on earthquakes and the times for their registration all over the world. This was before computer processing was available, but the system was the same. With her cardboard cards and her oatmeal boxes, Inge reglstered the velocity of propagation of the earthquakes to all parts of the globe. By means of this information, she deduced new theories of the inner parts of the Earth.

He further comments that there were not many Danish women who gained the international scientific celebrity status of Inge Lehmann:

It was not easy for a woman to make her way into the mathematical and scientific establishment in the first half of the twentieth century. As she said, 'You should know how many incompetent men I had to compete with-in vain.' Inge was probably not always very diplomatic. Nevertheless, she obtained great scientific results.

Lehmann always liked stimulating conversation and intelligent debate. She saw the need for constructive criticism and was impatient of the second-rate. She had a great physical energy, enjoying many mountaineering and skiing trips to the Alps and the mountains of Norway. She sometimes seemed to want to have a little less dignified lifestyle than the one that fate had produced for her, but at other times she was, to say the least, set in her ways. Inge Lehmann had an enormous fund of knowledge and experience about seismology from its early days in this century; in retrospect, it is a great shame that more effort was not made to persuade her to write up her reminiscences in more detail (28).

She participated in a reception held at the Danish Geodetic Institute on her l00th birthday in 1988. A large number of geophysicists from both sides of the Atlantic participated. Professors C. Kisslinger and V. Keilis-Borok gave speeches describing her achievements. Later she enjoyed relistening to a tape-recording of them. The Danish seismologist, Dr Erik Hjortenberg, her friend for many years, was invited to visit Inge in her beloved summer cottage in 1990, and admired how she could answer the phone as if nothing had changed, but, in fact, being almost blind, she needed a lot of help to move around. There can be no doubt that her almost 105 years were unusually stimulating and creative; Nils Groes writes, 'One day at the hospital, Inge told us that all day she had been thinking about her own life and she was content. It had been a long and rich life full of victories and good memories.' Those of us who were fortunate to know her as a scientist and friend can only confirm her own assessment.

In writing this Memoir, I have benefited from much advice and help from many friends and colleagues of Inge Lehmann. Many people favoured me with reminiscences and anecdotes from their encounters and association with her. I am specially grateful to Dr Erik Hjortenberg who contributed greatly to an earlier memoir. I also thank Lady Jeffreys, Dr Jack Oliver and Dr J. Taaghold for helpful information.

Biographical Memoirs

HONOURS

Inge Lehmann was one of the founders in 1936 of the Danish Geophysical Society and chaired the organization in 1941 and 1944. She was elected the first President of the European Seismological Federation in 1950, and served as a member of the Executive Committee of the International Association of Seismology and Physics of the Earth's Interior (Vice-President, 1963-67). She was elected Associate of the Royal Astronomical Society, London, in 1957, Honorary Fellow of the Royal Society of Edinburgh in 1959, and Foreign Member of the Royal Society, London, in 1969. Perhaps because she had no Ph.D., she was particularly proud of the honorary degrees of Doctor of Science at Columbia University in 1964 and D.Phil. of the University of Copenhagen in 1968. She received several honours and medals from international societies, including honorary membership of the European Geophysical Society in 1973, and the Bowie Medal of the American Geophysical Union in 1971, given for outstanding contributions to fundamental geophysics and unselfish cooperation in research. A unique honour was the receipt of the Danish Tagea Brandt award twice. A complete list of awards is given below.

Her name will continue to be honoured in the geophysical world. In 1996 the American Geophysical Union established the Inge Lehmann Medal. It will be given for 'outstanding contributions toward the understanding of the structure, composition and/or dynamics of the Earth's mantle and core'. It will be awarded not more than every other year in odd-numbered years. It is of interest that the A.G.U. chose to associate the medal with a much broader geophysical research scope than Lehmann's own seminal seismological discovery of a major Earth structure.

In her centennial year, two colleagues and I raised the question of the most appropriate way to name a major structural discontinuity (Anderson et at 1987) in the Earth after her. The inner-core boundary (ICB) is one of the three first-order seismo-compositional discontinuities that divide the Earth into crust, mantle, outer core and inner core. The other two discontinuities are well known by names of their discoverers, Andrija Mohorovicic and Beno Gutenberg. In this tradition, the ICB should be called the Lehmann Discontinuity in honour of its discoverer. The case was complicated because this title had already appeared in the literature (e.g. Anderson 1979, 1981) informally with respect to a discontinuity she inferred in the upper mantle at a depth of about 220 km. As outlined above, Lehmann's work on discontinuities in the upper mantle stems from 1953 and later (15, 18), but she proposed (8) the inner-core model 17 years before. In fact, the use of her name for structural features in the upper mantle has been sparse. We thus felt it most fitting that precedence should be accorded the earlier inference of the inner core, which is a feature of more central importance in the dynamic Earth.

AWARDS

1936-48: Member of the Executive Committee of the International Seismological Association.

1938: Tagea Brandt Award.

1951-54; 57-60: Member of the Executive Committee of the International Association of Seismology and Physics of the Earth's Interior.

1957: Associate Royal Astronomical Society, London.

1959: Honorary Fellow Royal Society, Edinburgh.

1960: The Harry Oscar Wood Award in Seismology.

1963-67: Vice-President of the Executive Committee of the International Association of Seismology and Physics of the Earth's Interior.

1964: Doctor of Science (Sc.D.) h.c. Columbia University in the City of New York.

1964: Deutsche Geophysikalische Gesellschaft, Emi-Wiechert Medal.

1965: Kgl. Danske Videnskabernes Selskab (Royal Danish Academy of Sciences and Letters) Gold Medal.

1967: Tagea Brandt Award.

1968: Doctor of Philosophy (Dr.phil.) h.c. University of Copenhagen.

1969: Foreign Member Royal Society, London.

1977: Medal of the Seismological Society of America.

REFERENCES TO OTHER AUTHORS

Anderson, D.L. 1979 The deep structure of the continents. J. Geophys. 84, 7555.

Anderson, D.L. 1981 Discontinuities in the mantle (Abstract). EOS 62, 1073.

Anderson, D.L., Bolt, B.A. & Morse, S.A. 1987 The Lehmann discontinuity. EOS 68, 1593.

Birch, F. 1940 The alpha-gamma transformation of iron at high pressure, and the problem of the Earth's magnetism. Am. J. Sci. 235, 192.

Bolt, B.A. 1962 Gutenberg's early PKP observations. Nature 196, 121.

Bolt, B.A. 1976 Nuclear explosions and earthquakes. The parted veil. New York: W.H. Freeman.

Bolt, B.A. 1987 50 years of studies on the inner core. EOS 68, 80.

Bolt, B.A. & Qamar A. 1970 An upper bound to the density jump at the boundary of the Earth's inner core. Nature 228, 148.

Brush, S.G. 1980 Discovery of the Earth's core. Am. J. Phys. 48, 705.

Bullen, K.E. 1946 A hypothesis on compressibility at pressures of the order of a million atmospheres. Nature 157, 405.

Dziewonski, A.M. & Anderson, D.L. 1981 Preliminary reference Earth model. Phys. Earth Planet Inter. 25, 297.

Engdahl, E.R., Flinn, E.A. & Romney,C.E 1970 Seismic waves reflected from the Earth's inner core. Nature 228, 852.

Gutenberg, B. 1914 Über Erdbebenwellen VIIA. Nachr. Ges. Wiss. Göttingen Math. Physik. Kl, 166.

Gutenberg, B. & Richter, C.F. 1938 P' and the Earth's core. Mon. Not. R. Astr Soc. Geophys. Suppl. 4, 363.

Jeffreys, H. 1939 The times of the core waves. Mon. Not R. Astr Soc. Geophys. Suppl. 4, 594.

Jeffreys, H. & Bullen, K.B. 1935 Times of transmission of earthquake waves. Bur Centr Seism. Internat. A., Fasc. II, 202 pp.

Song, X.D. & Richards, P. 1996 Seismological evidence for differential rotation of the Earth's inner core. Nature 382, 221.

Tromp, J. 1995 Normal-mode splitting observations from the great 1994 Bolivia and Kuril Islands earthquakes: Constraints on the structure of the mantle and inner core. GSA Today 5, 137.

Biographical Memoirs

BIBLIOGRAPHY

The following publications are those referred to directly in the text. A full bibliography appears on the accompanying microfiche, numbered as in the second column. A photocopy is available from the Royal Society Library at cost. This list is based on several personal files. Many incidental writings are not generally available and abstracts have been excluded. Some of the former are early Institute reports (in Danish) and the available abstract list is very incomplete. Quotations of Inge Lehmann are from her R.A.S. autobiographical notes unless otherwise attributed.

(1)/(4) 1929 ScPcS. Beitr. Geophys. 23, 369-378.

(2)/(5) 1930 P' as read from the records of the earthquake of June 16th 1929. Beitr. Geophys. 26, 402 412. Medd. Geod. Inst. Kobenhavn no. 1.

(3)/(6) 1930 A hammer for the Galitzen vertical component pendulum. Beitr. Geophys. 26, 413-415.

(4)/(9) 1931 Die Bedeutung der Europäischen Stationsgruppe für die Bestimmung von seismischen Laufzeitkurven. Verhandl. Fünften Tagung Balt. Geod Combustion, 192-212, Helsinki.

(5)/(10) 1932 Untersuchung der Europäischen Registrierungen der Erdbeben vom 18.VIII.1928, 24.X.1930 und 13.XI.1925 (with G. Plett). Beitr.Geophys. 36, 38-77. Medd. Geod. Inst. Kobenhavn no. 4.

(6)/(11) 1934 Transmission time for seismic waves for epicentral distances around 20°. Medd. Geod. Inst. Kobenhavn no. 5.

(7)/(12) 1935 Seismic time-curves for epicentral distances around 80°. The Aleutian earthquake of 1929, July 7th. Publ. Bur Cent. Seism. Int. A 12 109-133.

(8)/(13) 1936 P', Publ. Bur Cent. Seism. Int. A 14, 87-115.

(9)/(14) 1937 Seismic time-curves and depth determination. Mon. Not R. Astr Soc. Geophys. Suppl. 4, 250-271.

(10)/(21) 1948 On two explosions in Danish waters in the autumn of 1946. Geofis. Pur Appl. 12, 3-19.

(11)/(22) 1949 The reliability of the European seismological stations, Medd. Geod. Inst. Kobenhavn, no. 22.

(12)/(23) 1949 Den mikroseismiske uro og vejret. Naturens Verden 162-185. Kobenhavn.

(13)/(24) 1952 On the microseismic movement recorded in Greenland and its relation to atmosphenc disturbances. Ponteficiae Acad. Scient. Scripta Varia 23, 73-109.

(14)/(25) 1953 On the short-period surface wave Lg and crustal structure. IUGG Newsletter 2, 248-250. Lamont Geolog. Obs. Contr. 73.

(15)/(26) P and S at distances smaller than 25°. Trans. Am. Geophys. Un. 34, 477-483.

(16)/(30) 1955 The times of P and S in northeastern America. Annali Geofis. VIII, 351-370.

(17)/(35) 1957 On Lg as read in North American records. Annali Geofs. X, 1-21. Lamont Geolog. Obs. Contr. 222.

(18)/(38) 1959 Velocities of longitudinal waves in the upper part of the Earth's mantle. Annali Geofis. 15, 93-118. Dom. Obs. Ottawa, XIX, 10.

(19)/(42) 1961 S and the structure of the upper mantle. Geophys. Jl R. Astr Soc. 4. The Earth today, dedicated to Sir Harold Jeffreys, 124-138. Lamont Geolog. Obs. Contr. 449.

(20)/(43) 1962 The travel times of the longitudinal waves of the Logan and Blanca atomic explosions and their velocities in the upper mantle. Bull. Seism. Soc. Am. 52, 519-525.

(21)/(44) Recent studies of body waves in the mantle of the Earth. Q. Jl R. Astr. Soc. 3, 288-298.

(22)/(45) 1964 On the travel times of P as determined from nuclear explosions. Bull. Seism. Soc. Am. 54, 123-139. Lamont Geolog. Obs. Contr. 674.

(23)/(50) 1967 On the travel times of P as obtained from the nuclear explosions Bilby and Shoal. Phys. Earth Planet Interiors 1, 14-23. Lamont Geolog. Obs. Contr. 1097.

(24)/(53) 1968 Discontinuous velocity changes in the mantle as derived from seismic travel times and amplitudes. Bur Centr. Seism. Int. A 24, 167-174.

(25)/(54) 1969 Travel times and amplitudes of the Salmon nuclear explosion. Bull. Seism. Soc. Am. 59, 959-966. Lamont Geolog. Obs. Contr. 1309.

(26)/(55) 1969 Discontinuous velocity changes in the mantle as derived from seismic travel times and amplitudes. Publ. But: Cent. Seism. Int. A 24, 167-174.

(27)/(57) 1970 The 400 km discontinuity. Geophys. Jl R. Astr Soc. 21, 359-372.

(28)/(58) 1987 Seismology in the days of old. EOS 68, 33-35.